Direct numerical simulation of vertically heated natural convection over 3D irregular roughness

Natural convection in a cavity having an aspect ratio of 4 with irregular roughness on vertical isothermal sidewalls is investigated through compressible direct numerical simulation at a Rayleigh number of 1 × 10¹⁰. The compressible solver combined with the immersed boundary adopted in this paper is validated. The profiles of probability density functions of the thermal and hydrodynamic quantities show that at this Rayleigh number, the roughness increases the instability of the nearby fluid. In the instantaneous results, the isosurfaces of the Q-criterion reveal that a vortex is generated near roughness peaks and increases the local heat transfer, but in the valley regions, it is difficult to find vortex structures like in the peak regions. Results for the quasi-steady state show that the cavity with rough sidewalls has a lower Nusselt number on the hot wall than the smooth cavity. In other words, the roughness adversely affects the wall heat transfer. This indicates that the hot sidewall with roughness conveys less energy than the smooth wall. As a consequence, the fluid in the cavity with rough sidewalls has lower wall shear stress than that with smooth sidewalls. However, the results of the eddy heat flux show that turbulent flows generated by roughness enhance the heat transfer near the sidewalls. As the mixing effects of turbulent flows strengthen, the disparity of the average Nusselt number at the sidewall between rough and smooth cases reduces.